SOLVING INEQUALITIES5 9x

Step 1: Subtract 5 from both sides

5 5 9 5x

Step 2: Make a Clean Sweep

14x Final Answer

5 5 9 5x

+5 – 5 equals 0, leaving “x” all by itself=)

Since -9 and -5 have the same sign, add their

absolute values.

Since the numbers are both negative, the answer is

negative.

9 5 14

14

SOLVING INEQUALITIES5 6x

Step 1: Divide both sides by -55 65 5x

Step 2: Make sure to change inequality sign

11.2 or 1

5x x Final Answer

Divide by -5 because: -5 and x are involved in multiplying… The opposite of multiplying is dividing

5 65 5x

Step 3: Make a Clean Sweep

Change inequality sign whenever

MULTIPLYING OR DIVIDING by a

NEGATIVE number=)

5 65 5x

The -5’s divide out, leaving “x” by itself.

When dividing a negative number by a negative number, the answer is positive.

SOLVING INEQUALITIES4

7b

Step 1: Multiply both sides by 7

7 4 77b

Step 2: Make a Clean Sweep

28b Final Answer

Multiply both sides by 7 because: 7 and b are involved in division… The opposite of dividing is multiplying.

7 4 77b

The 7’s divide out, leaving “x” by itself.

A negative times a positive equals a negative so -4 times 7 is -28.

SOLVING INEQUALITIES8

4w

Step 1: Multiply both sides by -4

4 8 44w

Step 2: Make sure to change inequality sign

32b

Final Answer

Multiply both sides by – 4 because: -4 and w are involved in division… The opposite of dividing is multiplying

4 8 44w

Step 3: Make a Clean Sweep

Change inequality sign whenever

MULTIPLYING OR DIVIDING by a

NEGATIVE number=)

4 8 44w

The -4’s divide out, leaving “x” by itself.

A positive times a negative equals a negative.

8 times -4 is -32.

SOLVING INEQUALITIES4 2 30c

Step 1: Subtract 2 from both sides4 2 2 30 2c

Step 2: Divide both sides by 4

7c

Final Answer

Perform adding and subtracting first

when solving 2-step inequalities=)

Subtract 2 from both sides because: 2 is involved addition and the opposite of adding is subtracting=)

Divide by 4 because: 4 and c are involved in multiplying… The opposite of multiplying is dividing

4 2 2 30 2c

+2 -2 =0, leaving “4c” by itself.

30 – 2 = 28

4 28c

4 284 4c

Step 3: Make a Clean Sweep4 284 4c

The 4’s divide out, leaving “c” by itself.

28 divided by 4 equals 7.

SOLVING INEQUALITIES

Step 1: Add 9 to both sides3 9 9 12 9d

Step 2: Divide both sides by -3

7d Final

Answer

Perform adding and subtracting first

when solving 2-step inequalities=)

Add 9 to both sides because: 9 is involved subtraction and the opposite of subtracting is adding=)

Divide by -3 because: -3 and d are involved in multiplying… The opposite of multiplying is dividing

-9 +9 =0, leaving “-3d” by itself.

12 + 9 = 21

3 21d

3 213 3d

Step 3: Make a Clean Sweep3 213 3d

The -3’s divide out, leaving “d” by itself.

A positive divided by a negative equals a negative

21 divided by -3 equals -7.

3 9 12d

3 9 9 12 9d

Change inequality sign whenever

MULTIPLYING OR DIVIDING by a

NEGATIVE number=)

SOLVING INEQUALITIES3 7 1 31y y

Step 1: Combine Like Terms 3 7 1 31y y

Step 3:Divide by 4 & Make a Clean Sweep

8y Final Answer

Add 1 to both sides because: 1 is involved subtraction and the opposite

of subtracting is adding=)

We change inequality sign whenever we

MULTIPLY OR DIVIDE by a NEGATIVE

number=)

Step 2: Add 1 to Both Sides

3y and -7y are like terms.

Since 3y and -7y have opposite signs, we subtract the coefficients. (3 and -7 are the coefficients) 3 7 4

The answer keeps the sign of the integer with the larger absolute value

4 1 31y

4 1 31

4 1 1 31 1

y

y

-1 +1 =0, leaving “-4y” by itself.

31 + 1 =32

4 32y

4 324 4y

The -4’s divide out, leaving “y” by itself.

A positive divided by a negative equals a negative. 32 divided by -4 equals -8.

SOLVING INEQUALITIES8 2 9 1a a

8 2 9 1a a

Step 2: Divide both sides by 10

1a

Final Answer

Step 1: Combine Like Terms

Divide by 10 because: 10 and a are involved in multiplying… The opposite of multiplying is dividing

8a and 2a are like terms so we add the coefficients. 8 + 2 =10

9 and 1 are both integers so we add them. 9 + 1 =10

10 10a

10 1010 10a

Step 3: Make a Clean Sweep

10 1010 10a

The 10’s divide out, leaving “a” by itself.

10 divided by 10 equals 1.

SOLVING INEQUALITIES2 7

6x

Step 1: Subtract 2 from both sides

2 2 7 26x

Step 2: Multiply both sides by 6

54x

Final Answer

Perform adding and subtracting first

when solving 2-step inequalities=)

Multiply by 6 because: 6 and x are involved in dividing… The opposite of dividing is multiplying

+2 - 2 =0, leaving “x/6” by itself.

Since -7 and -2 have the same sign, add their

absolute values. 7 2 9Since the numbers are both

negative, the answer is negative.

9 9

6x

6 9 66x

Step 3: Make a Clean Sweep

6 9 66x

6 divided by 6 is 1.

1x=x

A negative times a positive equals a negative.

-9 times 6 = -54

SOLVING INEQUALITIES

Step 1: Add 5 to both sides

5 5 5 54x

Step 2: Multiply both sides by -4

40xFinal Answer

Perform adding and subtracting first

when solving 2-step inequalities=)

Multiply by -4 because: -4 and x are involved in dividing… The opposite of dividing is multiplying

-5 + 5 =0, leaving “x/-4” by itself.

5 + 5 = 10

104x

4 10 44x

Step 3: Make a Clean Sweep

4 10 44x

4 divided by 4 is 1.

1x=x

A positive times a negative equals a negative.

10 times -4 = -40

5 54x

We change inequality sign whenever we

MULTIPLY OR DIVIDE by a NEGATIVE

number=)

SOLVING INEQUALITIES( 5) 15b

Step 1: Distribute the negative sign to each term inside the parenthesis. 1( 5) 15b

Step 2: Subtract 5 from both sides.

10b

Final Answer

1( ) ( 1)( 5) 15b

1 5 15b

1 5 5 15 5b

1 10b

Step 4: Make a Clean Sweep

We change inequality sign whenever we

MULTIPLY OR DIVIDE by a NEGATIVE

number=)

Another way to write the negative sign is as a -1=)

Step 3: Divide both Sides by -1

+5 - 5 =0, leaving “-1b” by itself.

15 - 5 = 10

1 101 1b

1 101 1b

The -1’s divide out, leaving “b” by itself.

A positive divided by a negative equals a negative. 10 divided by -1 equals -10